Re: How is this inaccurate?

Originally Posted by Connie

I've been confronted by a parent who stated that my statements below are wrong
Please can you advise why?Use four digit whole numbers with two decimal places..
4567.89 rounded equals 4567.9 then 4568.09876.54 rounded equals 9876.50 then 9877.0

I see nothing wrong with the statements.
But all depends upon definition. How do you define rounding?
It appears that by round you mean to the closest integer.
If that is the case, and the decimal part is at least half round up.

Re: How is this inaccurate?

Originally Posted by Plato

I see nothing wrong with the statements.
But all depends upon definition. How do you define rounding?
It appears that by round you mean to the closest integer.
If that is the case, and the decimal part is at least half round up.

Thank you for your prompt response.

The individual stated that my use of the word equals was wrong.
Then they commented that the statement '4567.89 rounded equals 4567.9' was incorrect.

To put this in context this was the text that I sent home:Your maths mission for this week is to practise and improve your skills at rounding numbers to the nearest 1, 10, 100, or 1000.

Remember, when using whole numbers, look at the units. If the unit value equals 0 or 1 or 2 or 3 or 4 (less than 5) then round down:
72 rounded equals 70 because the 2 units is less than 5
654 rounded equals 650 because the 4 units is less than 5
9753 rounded equals 9750 because the 3 units is less than 5

If the unit value equals 5 or 6 or 7 or 8 or 9 (more than 4) then round up:
56 rounded equals 60 because the 6 units is more than 4
345 rounded equals 350 because the 5 units is more than 4
4567 rounded equals 4570 because the 7 units is more than 4

If you want a challenge then use four digit whole numbers with two decimal places.
4567.89 rounded equals 4567.9 then 4568.0
9876.54 rounded equals 9876.50 then 9877.0

Re: How is this inaccurate?

Originally Posted by Connie

Thank you for your prompt response.
The individual stated that my use of the word equals was wrong.
Then they commented that the statement '4567.89 rounded equals 4567.9' was incorrect.
To put this in context this was the text that I sent home:Your maths mission for this week is to practise and improve your skills at rounding numbers to the nearest 1, 10, 100, or 1000.
Remember, when using whole numbers, look at the units. If the unit value equals 0 or 1 or 2 or 3 or 4 (less than 5) then round down:
72 rounded equals 70 because the 2 units is less than 5
654 rounded equals 650 because the 4 units is less than 5
9753 rounded equals 9750 because the 3 units is less than 5
If the unit value equals 5 or 6 or 7 or 8 or 9 (more than 4) then round up:
56 rounded equals 60 because the 6 units is more than 4
345 rounded equals 350 because the 5 units is more than 4
4567 rounded equals 4570 because the 7 units is more than 4
If you want a challenge then use four digit whole numbers with two decimal places.
4567.89 rounded equals 4567.9 then 4568.0
9876.54 rounded equals 9876.50 then 9877.0

Frankly, I would avoid both the words rounded and equals.
I would ask, "what is the closest integer?".
On the other hand, the statement "The rounded form of 456.9 equals 457" is a very clear use of both words.

Re: How is this inaccurate?

There is nothing mathematically inaccurate about the algorithm you are teaching. But, that algorithm produces results that are undesirable in practical applications. Let's consider rounding to the unit, and compare the algorithm you are teaching to the algorithm of rounding to the nearest unit. For numbers with one digit after the decimal point, both algorithms yield the same results. For numbers with two digits after the decimal point, numbers ending with .45 to .49 round up using the algorithm you are teaching while they round down when rounding to the nearest unit. Assuming that in some practical application, numbers have equal chances of ending with any two digits, there is a 5% chance that any given number will round up using the algorithm you are teaching and down otherwise. Depending on the application, that can produce extremely significant differences in results.